Problem: What is the domain of the function $f(x)=\log_2(\log_3(\log_4x))$?
Explanation: In order for the given function to have a real value, $\log_3(\log_4x)>0$ (since the logarithm of only any positive number is real). In order for the last inequality to be true, $\log_4x>1$ (since the logarithm of only any number greater than 1 is greater than 0). The last inequality is true only if $x>4^1$, so $x>4$, or $x \in \boxed{(4, \infty)}$ in interval notation.